If sqrt {3x^2 - 7x - 30} + sqrt {2x^2 - 7x - | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $\sqrt {3x^2 - 7x - 30} + \sqrt {2x^2 - 7x - 5} = x + 5$Rearranging the terms: $\sqrt {3x^2 - 7x - 30} = (x + 5) - \sqrt {2x^2 - 7

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Given equation: $\sqrt {3x^2 - 7x - 30} + \sqrt {2x^2 - 7x - 5} = x + 5$Rearranging the terms: $\sqrt {3x^2 - 7x - 30} = (x + 5) - \sqrt {2x^2 - 7x - 5}$Squaring both sides:$3x^2 - 7x - 30 = (x + 5)^2 + (2x^2 - 7x - 5) - 2(x + 5)\sqrt {2x^2 - 7x - 5}$$3x^2 - 7x - 30 = x^2 + 10x + 25 + 2x^2 - 7x - 5 - 2(x + 5)\sqrt {2x^2 - 7x - 5}$$3x^2 - 7x - 30 = 3x^2 + 3x + 20 - 2(x + 5)\sqrt {2x^2 - 7x - 5}$$-10x - 50 = -2(x + 5)\sqrt {2x^2 - 7x - 5}$$5(x + 5) = (x + 5)\sqrt {2x^2 - 7x - 5}$Case $1$: $x + 5 = 0 \Rightarrow x = -5$. Checking in the original equation: $\sqrt{75+35-30} + \sqrt{50+35-5} = 0 \Rightarrow \sqrt{80} + \sqrt{80} = 0$, which is false.Case $2$: $5 = \sqrt {2x^2 - 7x - 5}$Squaring both sides: $25 = 2x^2 - 7x - 5$$2x^2 - 7x - 30 = 0$$(2x + 5)(x - 6) = 0$$x = 6$ or $x = -2.5$. Checking $x = 6$ in the original equation: $\sqrt{108-42-30} + \sqrt{72-42-5} = 6+5 \Rightarrow \sqrt{36} + \sqrt{25} = 11 \Rightarrow 6+5 = 11$. This is true.Thus, $x = 6$.

If $\sqrt {3x^2 - 7x - 30} + \sqrt {2x^2 - 7x - 5} = x + 5$, then $x$ is equal to

Similar Questions

The expression $x^2 + 2bx + c$ has a positive value for all real $x$ if:

If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$,where $a, b, c \in R$,have a common root,then $a:b:c = $ ...

Let $\alpha$ and $\beta$ be the roots of the equation $px^2 + qx + r = 0$ (where $p \neq 0$). If $p, q, r$ are in $A.P.$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

Solve the given equations and select the correct option.
$I.$ $8x + 7y = 135$
$II.$ $5x + 6y = 99$
$III.$ $9y + 8z = 121$

The equation $e^{\sin x} - e^{\sin(-x)} - 4 = 0$ has

Vedclass Test Series

Exam Paper Generator

Online Exam Module